In the -plane, what is the -intercept of the line whose equation is ?

Solution available with step-by-step explanation

SAT Linear Functions Question 139 | Free SAT Prep | Aniko

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Question 139·Easy·Linear Functions

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In the $xy$ -plane, what is the $y$ -intercept of the line whose equation is $5x + 3y = 12$ ?

For SAT questions asking for the y-intercept of a line, immediately set $x=0$ in the equation and solve for $y$ , then write the result as an ordered pair $(0,y)$ . This is usually faster and less error-prone than fully rearranging the equation into slope-intercept form, though converting to $y=mx+b$ is a good backup method if you are more comfortable with that format.

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Recall what a y-intercept is

The y-intercept is where the graph of the line crosses the y-axis. What must the $x$ -value be at that point?

Substitute into the equation

Once you know the $x$ -value at the y-intercept, plug that value into $5x + 3y = 12$ and simplify the equation.

Solve the simpler equation

After substitution, you should have an equation involving only $y$ . Solve this equation, then write the y-intercept as an ordered pair $(x,y)$ .

Desmos Guide

Graph the line

In Desmos, type the equation solved for $y$ , for example: y = (12 - 5x)/3. This will graph the line represented by $5x + 3y = 12$ .

Find the y-intercept on the graph

Look at the point where the line crosses the y-axis (where $x=0$ ). Click that point on the graph; Desmos will show its coordinates. The y-coordinate of this point is the y-intercept, and the full ordered pair is the answer.

Step-by-step Explanation

Use the definition of y-intercept

The y-intercept is the point where the line crosses the y-axis. On the y-axis, the $x$ -coordinate is always $0$ . So, to find the y-intercept of the line $5x + 3y = 12$ , we set $x=0$ .

Substitute $x=0$ and simplify

Replace $x$ with $0$ in the equation and simplify:

\begin{aligned} 5(0) + 3y &= 12 \\ 0 + 3y &= 12 \\ 3y &= 12 \end{aligned}

Now you have a simple equation in terms of $y$ only.

Solve for $y$ and write the intercept as a point

Solve $3y = 12$ to get $y = 4$ . The y-intercept is the point where $x=0$ and $y=4$ , so the y-intercept is $(0,4)$ .

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation