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How do you find the slope and y-intercept for the line $y = - \frac{7}{4} x + 2$ $y = -7/4 x +2$ ?

3 Answers

Sep 28, 2015

Slope: $- \frac{7}{4}$ $-7/4$
y-intercept: $2$ $2$

Explanation:

Any linear equation in the form
$XXX y = m x + b$ $color(white)("XXX")y = mx+b$
is in a form called the "slope-intercept form"
with a slope of $m$ $m$
and a y-intercept of $b$ $b$

$y = - \frac{7}{4} x + 2$ $y=-7/4x+2$ is in this form
with $m = - \frac{7}{4}$ $m= -7/4$
and a y-intercept $= 2$ $=2$

Sep 28, 2015

You do it like this:

Explanation:

A straight line is of the form:

$y = m x + c$ $y=mx+c$

$m$ $m$ is the gradient

$c$ $c$ is the intercept i.e the point at $x = 0$ $x=0$ where the line cuts the $y$ $y$ axis.

So for the line:

$y = - \frac{7}{4} x + 2$ $y=-7/4x+2$

The slope $m = - \frac{7}{2}$ $m=-7/2$ and the intercept $c = 2$ $c=2$ graph{y=-7/2x+2 [-10, 10, -5, 5]}

Sep 28, 2015

Slope= $- \frac{7}{4}$ $-7/4$

y-intercept= $2$ $2$

Explanation:

The coefficient of $x$ $x$ (that is, the number being multiplied by $x$ $x$ ) is the slope. Therefore, the slope= $- \frac{7}{4}$ $-7/4$

The y-intercept is the constant in the equation (that is, it is the number that is not being multiplied by any variable, such as $x$ $x$ or $y$ $y$ ). Therefore, the y-intercept= $2$ $2$

The equation of a line can generally be written as $y = m x + c$ $y=mx+c$ , where $m$ $m$ is the slope and $c$ $c$ is the y-intercept.

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