Answer:
(a) -2
(b) y -120 = -2(x -10)
(c) y = -2x +140
(d) 2x +y = 140
Step-by-step explanation:
Given a graph with y-intercept 140 and x-intercept 70, you want the slope and various equations describing the graph.
(a) Slope
The line drops from a y-value of 140 to 0 as x increases from 0 to 70. The slope is ...
m = rise/run = -140/70 = -2
The slope of the line is -2.
(b) Point-slope equation
The point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
We have a line with slope -2 that goes through the point (10, 120), so we can write the equation as ...
y -120 = -2(x -10)
(c) Slope-intercept form
In part (a) we identified the y-intercept as 140, so we can write the equation as ...
y = mx + b . . . . . line with slope m and y-intercept b
y = -2x +140 . . . . . . line with slope -2 and y-intercept 140
(d) Standard form
The slope-intercept equation can be converted to standard form by adding the opposite of the x-term to both sides.
y +2x = -2x +2x +140 . . . . . 2x added to both sides
2x +y = 140 . . . . . . . . . standard form equation of the line
