Question

PLEASE HELP!!!

A line passes through the point (4, 8) and has a slope of 3/2.

Write an equation in slope-intercept form for this line.

Answer 1

y=1.5x+2

Explanation:

The equation for a line in slope-intercept form is written as y=mx+c where m is the slope and cis the y-intercept.

We know the slope is 3/2 or 1.5, so we can write

y=1.5x+c

We know the line contains the point (4,8), so we can sub this in to find c:

8=1.5(4)+c

8=6+c

c=2

Having found m and c, we can write the equation:

y=1.5x+2

Answer 2

Answer:
`\text{y}=(3)/(2)\text{x}+2\\\\`

This is the same as writing y = (3/2)x + 2

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Work Shown:

`\text{y}-\text{y}_1=\text{m}\left(\text{x}-\text{x}_1\right)\\\\\text{y}-8=(3)/(2)\left(\text{x}-4\right)\\\\\text{y}-8=(3)/(2)\text{x}+(3)/(2)(-4)\\\\\text{y}-8=(3)/(2)\text{x}-6\\\\\text{y}=(3)/(2)\text{x}-6+8\\\\\text{y}=(3)/(2)\text{x}+2\\\\`

I used point-slope form as the first step. The 'm' is the slope, and
`(x_1,y_1) = (4,8)` is the point on the line.

The final step shows us the line has a y intercept of b = 2, which is at the location (0,2).

To graph this, draw a straight line through (0,2) and (4,8)

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Check:

Plug x = 4 into the equation we found. We should arrive at y = 8.

`\text{y}=(3)/(2)\text{x}+2\\\\\text{y}=(3)/(2)*4+2\\\\\text{y}=(12)/(2)+2\\\\\text{y}=6+2\\\\\text{y}=8\\\\`

This confirms (4,8) is indeed on this line and confirms the answer is correct.

You can also use graphing tools like Desmos or GeoGebra to quickly and visually confirm the answer.