Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #20 : How To Find Slope Of A Line

Determine the slope and y-intercept of the following equation.

Possible Answers:

None of these

Slope:

Y-intercept: 

Slope:

Y-intercept:

Slope:

Y-intercept:

Slope:

Y-intercept:

Correct answer:

Slope:

Y-intercept: 

Explanation:

You see that this equation is not written explicitly in terms of . Before we can determine the slope and y-intercept, we need to write the equation explicitly in terms of  by solving for .

First, add  to both sides.

Then subtract  to both sides.

Finally, divide by .

Now that the equation is explicitly in terms of , we can compare it to the general formula of a straight line in slope-intercept form.

In this equation, is equal to the slope and is equal to the y-intercept. Comparing our given equation to the formula, we can see that and .

Since the y-intercept is a point, we will want to write it in point notation: .

Example Question #21 : How To Find Slope Of A Line

There are two points:  and .

If these points are connected by a straight line, what is the slope of this straight line?

Possible Answers:

Correct answer:

Explanation:

To determine the slope, we use the following formula.

In the formula, the two points making up that slope are  and .  In our case, our two points are  and . Using these values in the formula allows us to solve for the slope.

The slope is .

Example Question #21 : How To Find Slope Of A Line

Find the slope of the line that passes through the points (0,2) and (5,-2).

Possible Answers:

Correct answer:

Explanation:

To find the slope of the line passing through the given points, we need to find the change in y and divide it by the change in x.  This can also be written as .  In our case, we have 

Example Question #23 : How To Find Slope Of A Line

Find the slope of the line using the following given points:

(2,5), (5,6), (8,7)

Possible Answers:

Correct answer:

Explanation:

To find the slope, divide the change in  by the change in .

So,

 

 

Check your answer by using the same equation on another pair of points:

It's the same! So the answer is .

Example Question #24 : How To Find Slope Of A Line

What is the y-intercept of the line 

Possible Answers:

Correct answer:

Explanation:

To easily determine an equation's y-intercept, convert it to the  form, where the  represents the equation's y-intercept.

Converting the given equation to this form gives you 

 

with a y-intercept of .

Example Question #25 : How To Find Slope Of A Line

The line given by the equation  has a slope of ______ and a y-intercept of ______.

Possible Answers:

Correct answer:

Explanation:

The equation  can be rearranged to slope-intercept form to give:

From here, it can be deduced that the slope is  and the y-intercept is .

Example Question #32 : Properties Of Functions And Graphs

What is the slope of the line depicted by this equation?

Possible Answers:

Correct answer:

Explanation:

This equation is written in standard form, that is, where the slope is equal to .

In this instance and

This question can also be solved by converting the slope-intercept form: .

Example Question #26 : How To Find Slope Of A Line

What is the slope of a line if the points on the line are  and ?

Possible Answers:

Correct answer:

Explanation:

Write the formula to find slope.

The values are interchangable as long as they are in the correct order.

The formulas yield similar slopes.   

The correct answer is .

Example Question #21 : How To Find Slope Of A Line

Fnd the slope of the following equation:

Possible Answers:

Correct answer:

Explanation:

To find the slope, we need to get the equation in the form of  to identify the value of the slope, .

Add  to both sides.

Divide both sides by 7.

.

Now we can see that our slope is the coefficient in front of the , which is just 1.

Example Question #3712 : Algebra 1

Find the slope of the following equation:

Possible Answers:

Correct answer:

Explanation:

Remember that the equation of a line is given as , where  is the slope and  is the y intercept.

To get out equation in that form so we can identify what our  is, we need to isolate  on one side and all other terms on the other side.

Now, to get just , divide both sides by 3.

.

Now, we can easily identify our slope as .

Learning Tools by Varsity Tutors