Find the slope intercept form and the point slope the line perpendicular to 4x-7y=2 going through (-6,1)

Slope-intercept form:

Point-slope-form:

Step-by-step explanation:

Hi there!

We want to find the equation of the line perpendicular to the line 4x-7y=2 that goes through (-6, 1) in slope-intercept form, as well as the point-slope form

Slope-intercept form is defined as y=mx+b, where m is the slope and b is the y intercept

Point-slope form is defined as , where m is the slope and is a point

Meanwhile, perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1

So let's find the slope of the line 4x-7y=2

The equation of the line is in standard form, which is ax+by=c, where a, b, and c are integer coefficients a is non-negative, and a and b aren't 0

So let's find the slope of the line 4x-7y=2

One way to do that is to convert the equation of the line from standard form to slope-intercept form

Our goal is to isolate y onto one side

Subtract 4x from both sides

-7y=-4x+2

Divide both sides by -7

y=

So the slope of the line 4x-7y=2 is

Now, we need to find the slope of the line perpendicular to it

Use this formula:

in this case is

Multiply both sides by

m=

Let's see the equation of the perpendicular line so far in slope-intercept form:

y=+b

We need to find b now

The equation of the line passes through (-6,1), so we can use it to solve for b.

Substitute -6 as x and 1 as y

Now multiply

1=

Subtract 42/4 from both sides to isolate b

-19/2=b

Substitute -19/2 as b into the equation

The equation in slope-intercept form y=

Now, here's the equation in point-slope form

Recall that the slope is , our point is (-6, 1), and point-slope form is

Let's label the value of everything to avoid any confusion

Now substitute those values into the equation

We can simplify the x--6 to x+6

Hope this helps!

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