How do you write an equation in slope intercept form given the slope and a point?

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How do you write an equation in slope intercept form given the slope and a point?

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Answer 1 · 2014-10-24T20:00:26

Slope Intercept form is y = mx + b, where
m = the slope and b = the y- intercept.

Slope is determined by formula

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2 - y_1)/(x_2-x_1)$

if you had the coordinates of two points on the line.

$(x_{1}, y_{1}) (x_{2}, y_{2})$ $(x_1,y_1) (x_2,y_2)$

b is the point at which the line will cross (intercept) the y-axis.

If a problem asked for the slope intercept form and provides a slope and a single point on the line you could find the equation with two different methods.

What is the slope intercept equation of a line with a slope of m = 3/4 and a point on the line of (4 , 5)?

The first method is to us the slope-intercept equation and plug in values to solve for b.

5 = $\frac{3}{4}$ $3/4$ (4) + b (simplify the fraction)

5 = 3 + b (isolate b)

5 - 3 = b (simplify)

b = 2

The slope-intecept equation would be y = $\frac{3}{4}$ $3/4$ x + 2

The second method is to use the point-slope formula

$(y - y_{1}) = m (x - x_{1})$ $(y - y_1) = m(x - x_1)$

Plug in the information and simplify for the equation.

$(y - 5) = \frac{3}{4} (x - 4)$ $(y - 5) = 3/4(x - 4)$ (distribute the slope)

$(y - 5) = \frac{3}{4} x - 3$ $(y - 5) = 3/4x - 3$ (isolate y)

$y = \frac{3}{4} x - 3 + 5$ $y = 3/4x - 3 + 5$ (simplify)

$y = \frac{3}{4} x + 2$ $y = 3/4x + 2$ is the slope-intercept equation.

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How do you write an equation in slope intercept form given the slope and a point?

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