Answer:
1.
x-intercept = 8/5
y-intercept = -4
m = 1.5 (or 5/2)
equation: y = 1.5x - 4
2.
x-intercept = -1/2
y-intercept = -3
m = -6
equation: y = -6x - 3
Useful things to note:
Definition of a y-intercept: The y value when x = 0.
Definition of a x-intercept: The x value when y = 0.
Definition of the slope-intercept form: y = mx + b
Explanation:
1.
We don't know the x-intercept yet, but we can easily find the y-intercept.
So on the x = 0 line, we see there's a point right at (0, -4). So, the y-intercept is at -4.
The other point that's given is (2, 1). This is useful for getting the slope-intercept form.
y = mx + b
Lets solve for m.
When solving for m in the slope-intercept form, we replace x and y with an available point. For this we'll use (2, 1). We already know that b = the y-intercept, which is -4. Combining these two facts, we get this equation:
1 = 2m - 4
Let's solve this:
1 = 2m - 4
1 + 4 = 2m -4 + 4
5 = 2m
5/2 = 2m/2
1 1/2 = m
or
1.5 = m
Now that we have m, we can easily get the equation!
b = -4
m = 1.5
replacing those in the slope-intercept formula, we get:
y = mx + b
y = (1.5)x + (-4)
equation: y = 1.5x - 4
in order to finally find the x-intercept, we find where x is when y = 0. (I'm going to use m = 5/2 for easiest convenience. All of those values work though :) )
y = 5/2x - 4
make y = 0
0 = 5/2x - 4
0 + 4 = 5/2x - 4 + 4
4 = 5/2x
4*(2/1) = 5/2x*(2/1)
8 = 5x
8/5 = 5x/5
8/5 = x
2.
We don't know the x-intercept yet, but we can easily find the y-intercept.
So on the x = 0 line, we see there's a point right at (0, -3). So, the y-intercept is at -3.
The other point that's given is (-1, 3). This is useful for getting the slope-intercept form.
y = mx + b
Lets solve for m.
When solving for m in the slope-intercept form, we replace x and y with an available point. For this we'll use (-1, 3). We already know that b = the y-intercept, which is -3. Combining these two facts, we get this equation:
3 = -1m - 3
Let's solve this:
3 = -1m - 3
3 + 3 = -1m -3 + 3
6 = -1m
6/-1 = -1m/-1
-6 = m
or
-6 = m
Now that we have m, we can easily get the equation!
b = -3
m = -6
replacing those in the slope-intercept formula, we get:
y = mx + b
y = (-6)x + (-3)
equation: y = -6x - 3
in order to finally find the x-intercept, we find where x is when y = 0.
y = -6x - 3
make y = 0
0 = -6x - 3
0 + 3 = -6x - 3 + 3
3 = -6x
3/(-6) = -6x/(-6)
-3/6 = x
simplify
-1/2 = x