# A line having a slope of 3/4 passes through the point (−8,4).Write the equation of this line in slope-intercept form.

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We are asked to find the equation of a line which contains (-8,4) as a point and has a slope of 3/4.

We will begin by writing the slope-intercept form.

=> y = mx + b

=> We will substitute the given point for x and y and the slope of 3/4 for m.  This will allow  us to find the y-intercept which is "b."

=> 4 = 3/4(-8) + b

=> 4 = -6 + b

=> 10 = b

Now we will place 3/4 into the slope-intercept form as m and 10 as b.

=> y = 3/4x + 10.

The equation of the line is y = 3/4x + 10.

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Let the required line be y = mx+c in the slope intercept form, where m is the slope and c is the y intercept.

We determine m and c by the using given conditions.

m = 3/4, given.

So y = (3/4)x+c (1).

The line at (1) has the point (-8, 4) on it.

Therefore  4 = (3/4)*(-8)+c...(2)

(1)-(2) gives: y-4 = (3/4)(x+8).

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

We  multiply 4  to get integral coefficients.

4(y-4) = 3x+24

We rearrange.

3x-4y+24+16= 0

3x-4y+40 = 0 is the required line.

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slope 3/4 passes through the point (−8,4)

The y-intercept form is y = mx + b where m is slope and b is the y-intercept.

Any easy path to this solution is to first right in point-slope form and solve for y.

point-slope formula: y - y1 = m(x - x1) where (x1, y1) is a point on your line and m is slope.

Plugging in:

y - 4 = .75(x - -8)

Solve for y and distribute the slope.

y - 4 = .75x + 6

y = .75x + 10