Write an equation for the line that is perpendicular to Y=-3/7x+4 and passes through (-4,-5)
1 answer:
9514 1404 393
Answer:
y = 7/3x +13/3
Step-by-step explanation:
The equation of the given line is in slope-intercept form (y=mx+b), so we can see the slope (m) is -3/7. The slope of the perpendicular line is the opposite reciprocal of this, so is ...
m = -1/(-3/7) = 7/3
The y-intercept of the perpendicular line can be found from ...
b = y -mx
b = -5 -(7/3)(-4) = -15/3 +28/3 = 13/3
Then the slope-intercept equation of the perpendicular line is ...
y = mx +b
y = 7/3x +13/3
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<em>Additional comment</em>
You can get there a little faster using the point-slope form of the equation of a line. For slope m and point (h, k) that form is ...
y -k = m(x -h)
For our perpendicular line, the equation is ...
y +5 = 7/3(x +4)
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Answer:
y = 10/9x + 9
Step-by-step explanation:
To write the equation in its slope-intercept form, y = mx + b, we need to find the slope (m) of the line and its y-intercept (b).
Given the points (0, 9) and (9, 19), we can solve for the slope of the line using the following formula:
Let (x1, y1) = (0, 9)
and (x2, y2) = (9, 19)
Substitute these values on the formula:
Therefore, the slope (<em>m </em>) = 10/9.
Next, the <u>y-intercept</u> is the point on the graph where it crosses the y-axis, and has the coordinates, (0, <em>b </em>). It is also the value of the y when x = 0.
One of the given points is the y-intercept of the line, given by (0, 9). The y-coordinate, 9, is the value of b.
Therefore, the linear equation in slope-intercept form is: y = 10/9x + 9