Question

What is the equation for a line with a slope of 4/5 that passes through the point (4,3)?

a) y = 4/5x - 3
b) y = 4/5x + 3
c) y = 3 - 4/5x
d) y = 3 + 4/5x

Answer 1

The equation of a line with a slope of 4/5 that passes through the point (4,3) is not one of the provided options. By using the point-slope form, we can derive the correct equation as y = (4/5)x - 1/5.

Step-by-step explanation:

To find the equation of a line with a given slope that passes through a specified point, you can use the point-slope form of a line's equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Since we have the slope m = 4/5 and the point (4, 3), we can plug these values into the point-slope form:

y - 3 = (4/5)(x - 4)

To find the equation in slope-intercept form (y = mx + b), we solve for y:

Distribute the slope 4/5 to both terms inside the parentheses:

y - 3 = (4/5)x - (4/5)×4

y - 3 = (4/5)x - 16/5

Now, add 3 to both sides to isolate y:

y = (4/5)x - 16/5 + 15/5
y = (4/5)x - 1/5

Thus, none of the given options a), b), c) or d) is correct. The equation for the line is y = (4/5)x - 1/5.