Question

Graphing in Point-Slope Form y−y1=m(x−x1)
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Graph the equation y+7=−45(x−4) ?

Answer 1

The graph is in the attachment.

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

m - slope

(x₁, y₁) - a point on a line

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept → (0, b)

We have the equation in a point-slope form:

`y+7=-(4)/(5)(x-4)`

`y-(-7)=-(4)/(5)(x-4)`

Therefore we have one point: (4, -7).

Convert to the slope-intercept form:

`y+7=-(4)/(5)(x-4)` use the distributive property

`y+7=-(4)/(5)x+\left(-(4)/(5)\right)(-4)`

`y+7=-(4)/(5)x+(16)/(5)`

`y+7=-(4)/(5)x+3(1)/(5)` subtract 7 from both sides

`y=-(4)/(5)x-3(4)/(5)`

Put x = -1 to the equation:

`y=-(4)/(5)(-1)-3(4)/(5)=(4)/(5)-3(4)/(5)=-3`

Therefore we have the second point (-1, -3).