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Precalculus : Graph a Linear Function

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Example Questions

Example Question #1 : Graph A Linear Function

Which of the following could be the function modeled by this graph?

Linearfxn

Possible Answers:

y=7x-5 $\displaystyle y=7x-5$

y=5x-7 $\displaystyle y=5x-7$

y=5x+7 $\displaystyle y=5x+7$

$y=\frac{1}{5}x-7$ $\displaystyle y=\frac{1}{5}x-7$

Correct answer:

y=5x-7 $\displaystyle y=5x-7$

Explanation:

Which of the following could be the function modeled by this graph?

Linearfxn

We can begin here by trying to identify a couple points on the graph

We can see that it crosses the y-axis at (0,-7) $\displaystyle (0,-7)$

Therefore, not only do we have a point, we have the y-intercept. This tells us that the equation of the line needs to have a $\displaystyle -7$ in it somewhere. Eliminate any option that do not have this feature.

Next, find the slope by counting up and over from the y-intercept to the next clear point.

It seems like the line goes up 5 and right 1 to the point (1,-2) $\displaystyle (1,-2)$

This means we have a slope of 5, which means our equation must look like this:

y=5x-7 $\displaystyle y=5x-7$

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Example Question #2 : Linear Functions

Find the slope of the linear function

$\displaystyle y-3=5(x+2)$

Possible Answers:

m=-3 $\displaystyle m=-3$

m=5 $\displaystyle m=5$

m=3 $\displaystyle m=3$

m=2 $\displaystyle m=2$

Correct answer:

m=5 $\displaystyle m=5$

Explanation:

For the linear function in point-slope form

$y-y_{1}=m\left ( x-x_{1}\right )$ $\displaystyle y-y_{1}=m\left ( x-x_{1}\right )$

The slope is equal to $\displaystyle m.$

For this problem

$\displaystyle y-3=5(x+2)$

we get

m=5 $\displaystyle m=5$

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Example Question #3 : Linear Functions

Find the slope of the linear function

$\displaystyle y-7=10(x+1)$

Possible Answers:

m=10 $\displaystyle m=10$

m=7 $\displaystyle m=7$

m=-7 $\displaystyle m=-7$

m=1 $\displaystyle m=1$

Correct answer:

m=10 $\displaystyle m=10$

Explanation:

For the linear function in point-slope form

$y-y_{1}=m\left ( x-x_{1}\right )$ $\displaystyle y-y_{1}=m\left ( x-x_{1}\right )$

The slope is equal to $\displaystyle m.$

For this problem

$\displaystyle y-7=10(x+1)$

we get

m=10 $\displaystyle m=10$

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Example Question #3 : Graph A Linear Function

What is the y-intercept of the line below?

$\displaystyle y = 3x + 4$

Possible Answers:

(0, 3) $\displaystyle (0, 3)$

(4,0) $\displaystyle (4,0)$

(0, 4) $\displaystyle (0, 4)$

(0, -3) $\displaystyle (0, -3)$

(3,0) $\displaystyle (3,0)$

Correct answer:

(0, 4) $\displaystyle (0, 4)$

Explanation:

By definition, the y-intercept is the point on the line that crosses the y-axis. This can be found by substituting x = 0 $\displaystyle x = 0$ into the equation. When we do this with our equation,

$y = 3x + 4 = 3\cdot0 + 4 = 0 + 4 = 4$ $\displaystyle y = 3x + 4 = 3\cdot0 + 4 = 0 + 4 = 4$.

Alternatively, you can remember $\displaystyle y = mx + b$ form, a general form for a line in which $\displaystyle m$ is the slope and $\displaystyle b$ is the y-intercept.

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Example Question #1 : Graph A Linear Function

What is the slope of the line below?

$y = \frac{2}{3}x + 6$ $\displaystyle y = \frac{2}{3}x + 6$

Possible Answers:

$\displaystyle 6$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$-\frac{2}{3}$ $\displaystyle -\frac{2}{3}$

$\displaystyle -6$

Correct answer:

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Explanation:

Recall slope-intercept form, or $\displaystyle y = mx + b$. In this form, $\displaystyle m$ is the slope and $\displaystyle b$ is the y-intercept. Given our equation above, the slope must be the coefficient of the x, which is $\frac{2}{3}$ $\displaystyle \frac{2}{3}$.

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Example Question #4 : Linear Functions

What is the x-intercept of the equation below?

$\displaystyle y = 3x - 6$

Possible Answers:

(-2, 0) $\displaystyle (-2, 0)$

$(\frac{1}{2}, 0)$ $\displaystyle (\frac{1}{2}, 0)$

(0, 2) $\displaystyle (0, 2)$

(0, -6) $\displaystyle (0, -6)$

(2,0) $\displaystyle (2,0)$

Correct answer:

(2,0) $\displaystyle (2,0)$

Explanation:

The x-intercept of an equation is the point at which the line crosses the x-axis. Thus, we can find the x-intercept by plugging in y=0 $\displaystyle y=0$. When we do this with our equation:

$y = 3x - 6 \rightarrow 0 = 3x - 6\rightarrow6 = 3x \rightarrow2 = x$ $\displaystyle y = 3x - 6 \rightarrow 0 = 3x - 6\rightarrow6 = 3x \rightarrow2 = x$

Thus, our x-intercept is the point (2,0) $\displaystyle (2,0)$.

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Precalculus : Graph a Linear Function

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Graph A Linear Function

Example Question #2 : Linear Functions

Example Question #3 : Linear Functions

Example Question #3 : Graph A Linear Function

Example Question #1 : Graph A Linear Function

Example Question #4 : Linear Functions

All Precalculus Resources

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