A line with slope passes through the point . What is the value of on this line when ?

Solution available with step-by-step explanation

SAT Linear Functions Question 28 | Free SAT Prep | Aniko

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Question 28·Easy·Linear Functions

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A line with slope $-3$ passes through the point $(0,4)$ . What is the value of $y$ on this line when $x=2$ ?

Your answer

(Express the answer as an integer)

When a line’s slope and a point with $x=0$ are given, immediately recognize that the point gives you the $y$ -intercept, so you can write the equation in slope-intercept form $y=mx+b$ very quickly. Plug the given $x$ -value into this equation and simplify carefully, paying close attention to negative signs; this is usually faster and less error-prone than trying to reason with the graph in your head.

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Use slope-intercept form

Think about the form of a line's equation that uses the slope and the $y$ -intercept directly. It looks like $y=mx+b$ .

Find the $y$ -intercept

In the point $(0,4)$ , what does the $0$ for $x$ tell you about this point's location on the graph? How does that help you find $b$ in $y=mx+b$ ?

Plug in the given $x$

Once you have the equation of the line, substitute $x=2$ into it and carefully simplify the resulting expression to find $y$ .

Desmos Guide

Graph the line

In Desmos, type the equation of the line using the given information: y = -3x + 4. This uses the slope $-3$ and the $y$ -intercept $4$ from the point $(0,4)$ .

Find the $y$ -value when $x=2$

Click on the wrench icon and add a table for the equation, or click directly on the graph and use the trace feature. In the table, enter $2$ in the $x$ -column and read off the corresponding $y$ -value; that $y$ -value is the solution.

Step-by-step Explanation

Write the equation of the line

Use slope-intercept form, $y=mx+b$ , where $m$ is the slope and $b$ is the $y$ -intercept.

The slope is given as $-3$ , so $m=-3$ .
The point $(0,4)$ lies on the line. When $x=0$ , the $y$ -value is the $y$ -intercept, so $b=4$ .

Therefore, the equation of the line is $y=-3x+4$ .

Substitute the given $x$ -value

You are asked for the value of $y$ when $x=2$ .

Use the equation $y=-3x+4$ and plug in $x=2$ :

y=-3(2)+4

Now simplify this expression step by step.

Simplify to find the corresponding $y$

Continue simplifying:

y=-3(2)+4=-6+4=-2

So, when $x=2$ , the value of $y$ on this line is $-2$ .

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