Questionthrough: $(-1, 4)$ , parallel to $y = -5x + 2$

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that's parallel to $y = -5x + 2$ and goes through the point $(-1, 4)$ . Watch out! Parallel lines have the same slope, so don't accidentally use a different one!
Also, make sure to use the given point correctly when finding the equation.

STEP 2

1. Find the Slope
2. Find the Equation

STEP 3

Alright, so we're given the equation $y = -5x + 2$ .
This equation is already in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 4

Looking at our given equation, we can see that the slope is $-5$ .
Since parallel lines have the same slope, our new line will also have a slope of $-5$ .
Awesome!

STEP 5

We know the slope is $-5$ and the line passes through the point $(-1, 4)$ .
We can use the point-slope form of a linear equation, which is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is the given point.

STEP 6

Let's plug in our values: $x_1 = -1$ , $y_1 = 4$ , and $m = -5$ .
So we have $y - 4 = -5(x - (-1))$ .

STEP 7

Now, let's simplify!
We have $y - 4 = -5(x + 1)$ .
Distributing the $-5$ gives us $y - 4 = -5x - 5$ .

STEP 8

Almost there!
To get the equation into slope-intercept form, we need to isolate $y$ .
We can do this by adding $4$ to both sides of the equation: $y - 4 + 4 = -5x - 5 + 4$ .

STEP 9

This simplifies to $y = -5x - 1$ .
And that's our final equation!

STEP 10

The equation of the line parallel to $y = -5x + 2$ and passing through the point $(-1, 4)$ is $y = -5x - 1$ .

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