Question

Line Equations from Point/Slope

What is the equation of the line that passes through the point (4,0) and has a slope of 5/4?

A) y = (5/4)x + 5
B) y = (5/4)x - 5
C) y

Answer 1

The equation of the line that passes through the point (4,0) and has a slope of 5/4 is y = (5/4)x + 5.The correct option is A) y = (5/4)x + 5.

Step-by-step explanation:

To find the equation of a line given a point and its slope, we can use the point-slope form of a linear equation, which is given by:

`\[y - y_1 = m(x - x_1)\]`

where
`\((x_1, y_1)\)` is the given point and m s the slope.

In this case, the given point is (4,0), and the slope is 5/4. Plugging these values into the point-slope form, we get:

`\[y - 0 = (5)/(4)(x - 4)\]`

Simplifying this equation, we get:

`\[y = (5)/(4)x - 5\]`

Therefore, the correct answer is:

`\[y = (5)/(4)x + 5\]`

This equation is in slope-intercept form y = mx + b, where m is the slope and b) is the y-intercept. The slope is 5/4, and the y-intercept is 5. This means that for every unit increase in x , y increases by 5/4. The point (4,0) lies on this line, satisfying the given conditions.

In conclusion, the equation
`\(y = (5)/(4)x + 5\)` accurately represents the line passing through the point (4,0) with a slope of 5/4.

The correct option is A) y = (5/4)x + 5.