What is the equation, in point-slope form, for a line that goes through (2, −6)and has a slope of −3/4 ?

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What is the equation, in point-slope form, for a line that goes through (2, −6)and has a slope of −3/4 ?

its y+1=8/9(x+4)

Y - y1 = m(x - x1)

slope(m) = -3/4

(2,-6)...x1 = 2 and y1 = -6

now we sub...pay close attention to ur signs

y - (-6) = -3/4(x - 2)...not done yet

y + 6 = -3/4(x - 2) <===

M = 4, x1 = –1, and y1 = –6

Formula for point-slope: [tex]y - y1 = m(x-x1)[/tex]

Plug in the values (1): [tex]y + 4 = -\frac{5}{6} (x - 8)[/tex] {Choice B}

Plug in the values (2): [tex]y + 6 = \frac{1}{3}(x+ 2)[/tex] {Choice C}

_______________________

[For (3) and (4) we need to solve for slope]

(3)

First, solve for slope.

Formula for slope: [tex]\frac{y2-y1}{x2-x1}[/tex]

Plug in values: [tex]\frac{-1-5}{-4-7} = - \frac{6}{11}[/tex]

Slope: [tex]- \frac{6}{11}[/tex]

Second, we must plug into point-slope form.

Formula for point-slope: [tex]y - y1 = m(x-x1)[/tex]

Plug in the values: [tex]y + 1 = - \frac{6}{11}(x + 4)[/tex] {Choice C}

(4)

First, solve for slope.

Formula for slope: [tex]\frac{y2-y1}{x2-x1}[/tex]

Plug in values: [tex]\frac{6-(-8)}{-4-7} = - \frac{14}{11}[/tex]

Slope: [tex]- \frac{14}{11}[/tex]

Second, we must plug into point-slope form.

Formula for point-slope: [tex]y - y1 = m(x-x1)[/tex]

Plug in the values: [tex]y - 6 = - \frac{14}{11}(x + 4)[/tex] {Choice D}

The equation that is in point-slope form for a line that goes through (2,-6) and has a slope of -3/4 is y+6=-3/4(x-2).

The equation for point-slope is y-y1=m(x-x1). So just take the given info and plug it in. Since the y-point is negative, it becomes a positive in the equation.

Y-y1=m(x-x1)

y+6 = -3/4(x -2)

y + 6 = -3/4x + 6/4

y = -3/4x + 6/4 - 6

y = -3/4x + 3/2 - 6

y = -3/4x + 3/2 - 4 4/2

y = -3/4x + - 4 1/2

y = -3/4x - 9/2

[tex](y + 6) = -\frac{3}{4}(x - 2)[/tex]

Step-by-step explanation:

Step 1: Use point-slope form

[tex](y - y_1) = m(x - x_1)[/tex]

[tex](y - (-6)) = -\frac{3}{4} (x - 2)[/tex]

[tex](y + 6) = -\frac{3}{4}(x - 2)[/tex]

[tex](y + 6) = -\frac{3}{4}(x - 2)[/tex]

If needed, solve for y to get slope-intercept form

[tex]y + 6 = -\frac{3}{4}x + \frac{3}{2} \\[/tex]

[tex]y + 6 - 6 = -\frac{3}{4}x + \frac{3}{2} -\frac{12}{2}[/tex]

[tex]y = -\frac{3}{2} x - \frac{9}{2}[/tex]

y+6=-3/4(x-2)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-6)=-3/4(x-2)

y+6=-3/4(x-2)

(y - (-6)) = -¾(x - 2)

y + 6 = -¾(x - 2)