Use the information given to determine the equation of each line.
a. the slope of the line is 4/3 and its y-intercept is -2
b.the line perpendicular to the line y=-2x+5 and passing through the point (-2,6)
This information may help you!
a.) y=mx+b so
b.)Perpendicular Lines Theorem
Two non-vertical lines are perpendicular if and only if their slopes are negative reciprocals.
a. To determine the equation of a line given the slope and y-intercept, you can use the slope-intercept form equation: y = mx + b, where m is the slope and b is the y-intercept.
For line a, the slope is 4/3 and the y-intercept is -2, so the equation would be:
y = (4/3)x - 2
b. To find the equation of a line perpendicular to another line, you need to determine the negative reciprocal of the original line's slope. Let's first rewrite the equation of the original line, y = -2x + 5, in slope-intercept form.
The slope-intercept form is y = mx + b, where the slope (m) is the coefficient of x and the y-intercept (b) is the constant term.
So, the original line has a slope of -2.
To find the negative reciprocal of -2, we flip the fraction and change the sign. So the negative reciprocal of -2 is 1/2.
Now, we know the slope of the new line, which is 1/2, and it passes through the point (-2,6).
Using the point-slope form, the equation of the new line would be:
y - 6 = (1/2)(x - (-2))
y - 6 = (1/2)(x + 2)
y - 6 = (1/2)x + 1
To put it in slope-intercept form, we isolate y:
y = (1/2)x + 7