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Algebra 1 : Functions and Lines

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Example Questions

Example Question #62 : How To Find The Equation Of A Line

Given the slope of a line is five, and a point on the graph is (5,3) , write the equation of the line in point-slope form.

Possible Answers:

y-3 = 5(x-5)

y+3 = 5(x+5)

y=5x+22

y=5x-22

y-3 = 5(x+5)

Correct answer:

y-3 = 5(x-5)

Explanation:

Write the formula for point-slope form.

y-y_1 = m(x-x_1)

The variable is the slope, and the point is in (x_1,y_1) format.

m=5

(x_1,y_1)=(5,3)

Substitute all the givens. There's is no need to simplify.

The answer is: y-3 = 5(x-5)

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Example Question #155 : Equations Of Lines

Given the slope is three, and a point is (3,3) on the graph, what is the equation of the line?

Possible Answers:

y=3x+3

y=3x-9

y=3x-6

y=3x-3

y=3x+6

Correct answer:

y=3x-6

Explanation:

Write the slope intercept form.

y=mx+b

Substitute the slope and the point to find the y-intercept, .

3=3(3)+b

Solve for the unknown variable.

3=9+b

Subtract nine from both sides.

-6=b

Write the equation now that we have the slope and y-intercept.

The answer is: y=3x-6

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Example Question #156 : Equations Of Lines

Find the equation of the line given two points: (1,9) and (-2,11)

Possible Answers:

$y=-\frac{4}{3}x+7\frac{5}{8}$

y=-x+10

$y=-x+9\frac{2}{3}$

$y=-\frac{2}{3}x+9\frac{2}{3}$

$y=-\frac{2}{5}x+8\frac{1}{3}$

Correct answer:

$y=-\frac{2}{3}x+9\frac{2}{3}$

Explanation:

Write the slope intercept form. The equation will be in this form.

y=mx+b

Write the slope formula.

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

Let (x_1,y_1)=(1,9) and (x_2,y_2)=(-2,11) .

Substitute the points into the slope formula.

$m = \frac{y_2-y_1}{x_2-x_1} = \frac{11-9}{-2-1} = \frac{2}{-3}$

The slope is: $-\frac{2}{3}$

Use the slope and a given point, substitute them into the slope intercept form to find the y-intercept.

$9=(-\frac{2}{3})(1)+b$

Solve for the y-intercept.

$9=-\frac{2}{3}+b$

Add two-thirds on both sides.

$9+ \frac{2}{3}=-\frac{2}{3}+b+ \frac{2}{3}$

Simplify both sides.

$b=9\frac{2}{3}$

With the slope and y-intercept known, write the formula.

The answer is: $y=-\frac{2}{3}x+9\frac{2}{3}$

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Example Question #157 : Equations Of Lines

Given the x-intercept is seven, and the y-intercept is four, what is the equation of the line?

Possible Answers:

$y=-\frac{7}{4}x+4$

$y=\frac{4}{7}x+4$

$y=-\frac{4}{7}x+4$

$y=\frac{7}{4}x+4$

$\textup{Not enough information.}$

Correct answer:

$y=-\frac{4}{7}x+4$

Explanation:

The x-intercept is the value when y=0 .

The y-intercept is the value when x=0 .

We know the two points needed to find the equation of the line.

The points are: (7,0) and (0,4)

Use the slope formula to find the slope.

$m=\frac{y_2-y_1}{x_2-x_1} = \frac{4-0}{0-7} = -\frac{4}{7}$

Write the slope-intercept equation.

y=mx+b

Substitute the slope and the y-intercept.

The answer is: $y=-\frac{4}{7}x+4$

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Example Question #158 : Equations Of Lines

If the slope is four, and a known point is (-5,2) , what is the equation in point-slope form?

Possible Answers:

y-2 = 4(x-5)

y-2 = 4(x+5)

y+2 = 4(x-5)

y=4x-22

y=4x+22

Correct answer:

y-2 = 4(x+5)

Explanation:

Write the equation in point-slope form.

y-y_1=m(x-x_1)

The variable is the slope. Substitute the slope and the point.

y-2 = 4(x-(-5))

Simplify the right side of the equation.

The answer is: y-2 = 4(x+5)

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Example Question #161 : Equations Of Lines

A line passes through the points (3, 9) and (5, 3), and has a y-intercept of 3. Which of the following is an equation for that line?

Possible Answers:

y = 8x-12

$\small y = 9x-6$

$\small y = -4x + 8$

y = -2x-4

$\small \small y = -{3}x + 3$

Correct answer:

$\small \small y = -{3}x + 3$

Explanation:

The equation for a line is always $\small y = mx + b$ , where $\small m = slope$ and $\small b = y-intercept$ .

Given two data points, we are able to find the slope, m, using the formula

$\small \frac{y_{1}-y_{2}}{x_{1}-x_{2}}$ .

Using the data points provided, our formula will be:

$\small \small \frac{3-9}{5-3}$ , which gives us $\small \small -\frac{6}{2} ,$ or , $\small \small m = -3$ .

Our y-intercept is given.

Thus our equation for the line containing these points and that y-intercept is $\small \small y = -{3}x + 3$ .

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Example Question #1 : How To Find Slope Of A Line

What is the slope of the equation 4x + 3y = 7?

Possible Answers:

–3/4

4/3

–7/3

–4/3

3/4

Correct answer:

–4/3

Explanation:

We should put this equation in the form of y = mx + b, where m is the slope.

We start with 4x + 3y = 7.

Isolate the y term: 3y = 7 – 4x

Divide by 3: y = 7/3 – 4/3 * x

Rearrange terms: y = –4/3 * x + 7/3, so the slope is –4/3.

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Example Question #1 : How To Find Slope Of A Line

Find the slope of the line through the points (6,2) and (3,4).

Possible Answers:

$\frac{3}{2}$

$\frac{2}{3}$

$-\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$-\frac{2}{3}$

Explanation:

The equation for slope is $\frac{(y_2-y_1)}{(x_2-x_1)}$ . You plug in the coordinates from the points given you, and get $\frac{(4-2)}{(3-6)}$ , giving you $\frac{2}{-3}$ . Note that it does not matter which point you use as point 1 and point 2, as long as you are consistent.

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

(6,2) = (x₁,y₁)

(3,4) = (x₂,y₂)

$\frac{(4-2)}{(3-6)}=\frac{2}{-3}=-\frac{2}{3}$

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Example Question #1 : How To Find Slope Of A Line

Given the line 4y = 2x + 1, what is the slope of this line?

Possible Answers:

–2

–1/4

1/2

1/4

Correct answer:

1/2

Explanation:

4y = 2x + 1 becomes y = 0.5x + 0.25. We can read the coefficient of x, which is the slope of the line.

4y = 2x + 1

(4y)/4 = (2x)/4 + (1)/4

y = 0.5x + 0.25

y = mx + b, where the slope is equal to m.

The coefficient is 0.5, so the slope is 1/2.

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Example Question #2 : How To Find Slope Of A Line

What is the slope of the line containing the points (7,12) and (91,32).

Possible Answers:

$\frac{44}{49}$

$\frac{3}{32}$

$\frac{5}{21}$

$\frac{51}{30}$

Correct answer:

$\frac{5}{21}$

Explanation:

To find the slope of a line you must first assign variables to each point. It does not matter which points get which variables as long as you keep the $x_{1}$ and $y_{1}$ and $x_{2}$ and $y_{2}$ consistent when you plug them into the equation.

Then we plug in the variables to this equation where represents the slope. $m=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$

Then we plug in our points for $x_{1},x_{2},y_{1},and\ y_{2}$ and the example looks like $m=\frac{(32-12)}{(91-7)}$

Then we perform the necessary subtraction and division to find an answer of $m=\frac{20}{84}=\frac{5}{21}$

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #62 : How To Find The Equation Of A Line

Example Question #155 : Equations Of Lines

Example Question #156 : Equations Of Lines

Example Question #157 : Equations Of Lines

Example Question #158 : Equations Of Lines

Example Question #161 : Equations Of Lines

Example Question #1 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #2 : How To Find Slope Of A Line

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