Identify the slope(m) and y-intercept(b):
y= -5x+4

answer: m=y2−y1x2−x1=(−1)−33−(−3)=−46=−23

we can find the b-value, the y-intercept, by looking at the graph

picture28

b = 1

we've got a value for m and a value for b. this gives us the linear function

y=−23x+1

in many cases the value of b is not as easily read. in those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.

we can use the example above to illustrate this. we've got the two points (-3, 3) and (3, -1). from these two points we calculated the slope

m=−23

this gives us the equation

y=−23x+b

from this we can solve the equation for b

b=y+23x

and if we put in the values from our first point (-3, 3) we get

b=3+23⋅(−3)=3+(−2)=1

if we put in this value for b in the equation we get

y=−23x+1

which is the same equation as we got when we read the y-intercept from the graph.

to summarize how to write a linear equation using the slope-interception form you

identify the slope, m. this can be done by calculating the slope between two known points of the line using the slope formula.

find the y-intercept. this can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

once you've got both m and b you can just put them in the equation at their respective position.

video lesson

find the equation to the graph

picture29

step-by-step explanation:

how is that middle school

step-by-step explanation: