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We will need to use point-slope form, and then put this into slope-intercept form. We can also use slope-intercept form, and plug in the coordinates but we should get the same answer.

Firstly, we need to find the slope. We can use the formula y2-y1/x2-x1. 1-(-3)/-3-1 is 4/-4. The slope is -1.

Next, point-slope form is y-y1=m(x-x1). I will use the coordinate (1, -3) for y1 and x1. M is the slope. We do not need to worry about y and x. y-(-3)=-1(x-1). This gives us y+3=-x+1. Once we subtract 3, to isolate y, we get y=-x-2.

The answer is y=-x-2
cinderofsoulsss

Answer:

[tex]y=-x-2[/tex]

Step-by-step explanation:

1) First, find the slope between these 2 points.

(1, -3)

(-3, 1)

The change between the y-values is 4.

[tex]1--3=1+3=4[/tex]

The change between the x-values is -4.

[tex]-3-1=-4[/tex]

Slope is rise over run, and this is a rise of 4 and a run of -4, so the slope is -1.

[tex]\frac{4}{-4}=1[/tex]

If you just wanted to use the slope formula, you could do that too:

[tex]m=\frac{y2-y1}{x2-x1}\\\\m=\frac{1--3}{-3-1}\\\\m=\frac{4}{-4}\\\\m=-1[/tex]

2) Second, now you can use the slope to calculate the y-intercept.

Pick whichever point you want, and plug it into the equation along with the slope and solve for b.

(1, -3) = (x, y)

[tex]y=mx+b\\-3=(-1)(1)+b\\-3=-1+b\\-2=b\\b=-2[/tex]

The y-intercept is -2.

3) Finally, you can wire the equation in slope-intercept form.

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept.

Plug in the values we found and you're done:

[tex]y=-x-2[/tex]

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