The equation -5x-3y=2 is a linear equation in standard form. From this equation, answer the following:a. Find the y and x-intercepts
b. Write this equation in slope-intercept form.
for the x-intercept, set y=0: -5x=2
for the y-intercept, set x=0: -3y=2
you want y=mx+b, so start with getting y on the left:
-3y = 5x+2
...
To find the y-intercept, we can set x = 0 and solve for y. Similarly, to find the x-intercept, we can set y = 0 and solve for x.
a. Finding the y-intercept:
Setting x = 0 in the equation -5x - 3y = 2, we have:
-5(0) - 3y = 2
-3y = 2
Dividing both sides by -3, we get:
y = 2/(-3)
y = -2/3
Therefore, the y-intercept is (0, -2/3).
b. Finding the x-intercept:
Setting y = 0 in the equation -5x - 3y = 2, we have:
-5x - 3(0) = 2
-5x = 2
Dividing both sides by -5, we get:
x = 2/(-5)
x = -2/5
Therefore, the x-intercept is (-2/5, 0).
To write the equation in slope-intercept form (y = mx + b), we need to isolate y on one side of the equation.
-5x - 3y = 2
Subtract -5x from both sides:
-3y = 5x + 2
Divide both sides by -3:
y = (-5/3)x - 2/3
Therefore, the equation -5x - 3y = 2 in slope-intercept form is y = (-5/3)x - 2/3.