Mathematics, 20.01.2021 22:20 fansofboys

What is the slope-intercept form of the equation of the line containing the point (-5, 1) and having the slope 7?

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Answer from: mathman783

y = 7x + 36

Step-by-step explanation: Slope intercept form is y = mx + b where your slope is m, your b is the y-intercept, and x and y are your plot points. To solve this you just plug in the numbers. We already know the slope is 7 so we have our m, now we plug in the coordinate (-5, 1) with -5 as x and 1 as y. Plug them in and now you have the equation 1 = 7(-5) + b. You want to solve for b. So you end up getting b= 36. Now you have your y intercept so your final equation is y = 7x + 36. Hope this helped!!

Answer from: Quest

its not b

step-by-step explanation:

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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