Question content area top Part 1 Write an equation in​ slope-intercept form n. ​(minus7​,minus5​); y equals negative 4 x plus 2

Answer 1

If you enter the equation in function format in Desmos:

f(x) = -4x + 2

and then enter f(-7) the result will be 30 which is not equal to -5. So ( -7 , -5 ) is not on this line.

Most likely, the whole problem either asks you to find a line parallel to the given line or perpendicular to it.

To find a line parallel to the given linecand passing through the given point, remember that parallel lines have the same slope. Then you can either use the slope-intercept form or the point-slope form to find the requested line.

The slope of the given line us equal to the coefficient of x in the slope-intercept form. We were given the slope-intercept form of the original equation, so the slope is -4. Let's use the slope-intercept form to find the y-intercept:

y = mx + b

Plug in the known values:

-5 = ( -4 ) * ( -7 ) + b

-5 = 28 + b

-33 = b

So the line parallel to the given line and passing through the given point is:

y = -4x -33

You can verify this by graphing both the line and the given point in Desmos, or by using the technique demonstrated above.

The other possible problem could be to find the line perpendicular to the given line and passing through the given point.

Perpendicular lines that are neither vertical nor horizontal have slopes that are negative recipricols to each other. (Some call this opposite reciprocals.)

In other words, the product of the slopes of slanted lines is-1. Vertical lines have an undefined slope, so we can't use it's negative reciprocal is also not defined. Instead, we recognize that vertical lines can be written in the form x = some number. Horizontal lines can be written in the form y = some number. Given any point any point on the given line, say

( a , b), then the vertical line equals the x values and the horizontal line equals the y value:

x = a and y = b.

For example if the point is ( 3 , 4 ), then

x = 3 and y =4.

As mentioned above, if the lines are neither vertical nor horizontal, the slopes of the lines are negative reciprocals and hence their product is -1.

Since the slope of the given line is -4, the slope of ANY line perpendicular to it must be 1/4.

y = mx + b

-5 = ( 1/4 ) * ( -7 ) + b

-5 = ( - 7 / 4 ) + b

-5 + 7/4 = b

-20/4 + 7/4 = b

-13/4 = -3.25 = b

So the line perpendicular to the given line passing through the given point is:

y = (1/4)x - 3.25

Once again, this can be verified by graphing in Desmos.

Answer 2

The equation y = -4x+2 is already in slope intercept form. I'm not sure what you're asking here.

If you are being asked if the point (-7, -5) lies on that line, plug in -7 for x in that equation, and solve for y to see if you get -5.

Use the Desmos graphing calculator to graph equations. It is a very helpful tool to show the concepts of slope and intercepts.