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Algebra 1 : Equations of Lines

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Example Questions

Example Question #110 : How To Find Slope Of A Line

What is the slope of the line that passes through the following points?

(76,-585) and (56,85)

Possible Answers:

33.5

-33.5

Correct answer:

-33.5

Explanation:

What is the slope of the line that passes through the following points?

(76,-585) and (56,85)

Calculate slope using the following formula:

$m=\frac{y_1-y_2}{x_1-x_2}$

Note that it isn't important which point you choose as "1" and which point you choose as "2." All that matters is that you keep it consistent.

$m=\frac{-585-85}{76-56}=\frac{-670}{20}=-33.5$

So our slope is -33.5

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Example Question #511 : Functions And Lines

Find the slope between (7,2) and (-3,-5) .

Possible Answers:

$m=\frac{10}{7}$

$m=\frac{}7{10}$

$m=\frac{2}{5}$

$m=\frac{5}{8}$

$m=\frac{5}{2}$

Correct answer:

$m=\frac{}7{10}$

Explanation:

To find the slope between two points, use the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$(x_{1},y_{1})=(7,2)$

$(x_{2},y_{2})=(-3,-5)$

Plug in these values into the slope formula and solve.

$m=\frac{-5-2}{-3-7}=\frac{-7}{-10}=\frac{7}{10}$

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Example Question #111 : How To Find Slope Of A Line

Find the slope of the line that travels through the points (4, 5) and (2, -3) .

Possible Answers:

$\frac{-1}{5}$

$\frac{1}{4}$

$\frac{-1}{4}$

Correct answer:

Explanation:

To find the slope of a line that travels through any two points, we always use the same formula:

$Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Any time we are given a set of points on a line, they are written out as follows: (x, y) . The value is always listed first, followed by the y value.

When you are given two sets of points, you can find the slope of the line that travels through the by plugging in the values you were given into the slope formula. Let's try it ourselves.

Pick one of the two sets of points that you were given as your starting point. It doesn't matter which set you start with, so let's use (4, 5) . is an value, and is a value; since this is the first set we chose, let's say is $x_{1}$ , and is $y_{1}$ . Let's plug these two values into our formula for now:

$Slope = \frac{y_{2}-5}{x_{2}-4}$

Now, let's fill in the rest of the formula with the values from our set set of points, (2, -3) .

Since we're using this set second, will be $x_{2}$ , and -3 will be $y_{2}$ :

$Slope = \frac{-3-5}{2-4}$

Now, we just need to simplify:

$Slope = \frac{-8}{-2} = \frac{-4}{-1} = 4$

So, the slope of our line is .

**Remember, it doesn't matter which set of points you use first or second, as long as you make sure you do not mix up the order that you use the values in. For example, if you used as $x_{2}$ , you MUST use as $y_{2}$ , NOT $y_{1}$ . Values that come from the same set of points must be used to replace variables with the same sub-value.

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Example Question #113 : How To Find Slope Of A Line

Find the slope of a line that connects points (4,5) and (-1,7) .

Possible Answers:

$\frac{5}{2}$

$\frac{1}{5}$

$-\frac{2}{5}$

$-\frac{2}{3}$

$-\frac{12}{5}$

Correct answer:

$-\frac{2}{5}$

Explanation:

The formula for the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

All we need to do is plug in our values and solve for m.

$x_{1}=4,y_{1}=5,x_{2}=-1,y_{2}=7,$

Therefore, to solve, we get

$\frac{7-5}{-1-4}=\frac{2}{-5}=-\frac{2}{5}$

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Example Question #114 : How To Find Slope Of A Line

A line passes through the points (9,1) and (4,2) . What is the slope?

Possible Answers:

$\frac{1}{5}$

$\frac{3}{13}$

$\frac{13}{3}$

$-\frac{1}{5}$

Correct answer:

$-\frac{1}{5}$

Explanation:

The slope of a line is a measure of the rate of change of the incline of a line. Slope is more commonly taught as "rise over run". This kind of problem can be easily solved for by using the simple formula for slope.

$m=\frac{\Delta y}{\Delta x} = \frac{rise}{run}={\color{Blue} \frac{y_2-y_1}{x_2-x_1}}$ , where $\small m$ denotes slope. Rise denotes change in the y-axis where run denotes change in the x-axis. This makes sense because rise indicates a vertical change while run indicates a horizontal change.

The given points may be arbitrarily assigned as (x_1,y_1) and (x_2,y_2) . For this problem we will assign (9,1) as and (4,2) as .

$\frac{y_2-y_1}{x_2-x_1}$

$\frac{2-1}{4-9}=\frac{1}{-5}$

Therefore, ${\color{Blue} m= - \frac{1}{5}}$

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Example Question #115 : How To Find Slope Of A Line

A line passes through the points (1,4) and (15,28) . What is the slope of the line?

Possible Answers:

$\frac{1}{14}$

$\frac{24}{7}$

$\frac{1}{4}$

$\frac{12}{7}$

Correct answer:

$\frac{12}{7}$

Explanation:

The given points may be arbitrarily assigned as (x_1,y_1) and (x_2,y_2) . For this problem we will assign (1,4) as $\small (x_1,y_1)$ and (15,28) as .

$\frac{y_2-y_1}{x_2-x_1}$

$\frac{28-4}{15-1}=\frac{24}{14}=\frac{12}{7}$

Therefore, ${\color{Blue} m= \frac{12}{7}}$

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Example Question #116 : How To Find Slope Of A Line

If a line passes through the points $\small (-4,-8)$ and $\small (7,12)$ , what is its slope?

Possible Answers:

$\frac{20}{11}$

$\frac{4}{3}$

$\frac{11}{20}$

$\frac{3}{4}$

$\frac{5}{6}$

Correct answer:

$\frac{20}{11}$

Explanation:

The given points may be arbitrarily assigned as $\small (x_1,y_1){}$ and $\small (x_2,y_2)$ . For this problem we will assign $\small (-4,-8)$ as $\small (x_1,y_1){}$ and $\small (7,12)$ as $\small (x_2,y_2)$ .

$\frac{y_2-y_1}{x_2-x_1}$

$\frac{12--8}{7--4}=\frac{20}{11}$

Therefore, ${\color{Blue} m= \frac{20}{11}}$

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Example Question #117 : How To Find Slope Of A Line

What is the slope, , of the line: 3y=6x+144

Possible Answers:

m=144

m=2

m=48

m=6

Correct answer:

m=2

Explanation:

To solve this question you must get the equation written in the y=mx+b formula.

To do this, you need to isolate the by dividing everything by . So you will get:

y=2x+48

in the slope-intercept equation is your slope, which in this equation is .

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Example Question #181 : Slope And Line Equations

Find the slope and y intercept of the following function:

2x+4y=10x-4

Possible Answers:

m=-2, b=-2

m=4, b=10

m=10, b=4

m=2, b=-1

m=-4, b=10

Correct answer:

m=2, b=-1

Explanation:

The easiest way to solve this porblem is to change it into slope-intercept form:

y=mx+b

where m is slope and b is the y intercept.

Combining like terms and isolating y:

2x+4y=10x-4

4y=8x-4

y=2x-1

Now our function is ins slope-intercept form and we can see that:

m=2, b=-1 .

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Example Question #119 : How To Find Slope Of A Line

A function is given as

3x-2y=1 .

Find the slope and the y-intercept of this function.

Possible Answers:

$slope=-3,\: intercept=-1$

$slope=3,\: intercept=1$

$slope=\frac{3}{2},\: intercept=-\frac{1}{2}$

None of the above. This is not a linear function.

$slope=\frac{3}{2},\: intercept=1$

Correct answer:

$slope=\frac{3}{2},\: intercept=-\frac{1}{2}$

Explanation:

The original function is is given in standard form,

Ax+By=C .

Convert this equation into slope-intercept form,

y=mx+b .

3x-2y=1

First subtract 3x from each side.

-2y=1-3x

Now divide by negative two to solve for y.

$y=-\frac{1}{2}+\frac{3}{2}x$

In slope intercept form the equation becomes,

$y=\frac{3}{2}x-\frac{1}{2}$ .

We know that, in slope-intercept form, the slope is given as "m" while the y-intercept is given as "b".

Therefore, the slope of this function is $m=\frac{3}{2}$ and the y-intercept is $b=-\frac{1}{2}$ .

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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #110 : How To Find Slope Of A Line

Example Question #511 : Functions And Lines

Example Question #111 : How To Find Slope Of A Line

Example Question #113 : How To Find Slope Of A Line

Example Question #114 : How To Find Slope Of A Line

Example Question #115 : How To Find Slope Of A Line

Example Question #116 : How To Find Slope Of A Line

Example Question #117 : How To Find Slope Of A Line

Example Question #181 : Slope And Line Equations

Example Question #119 : How To Find Slope Of A Line

All Algebra 1 Resources

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