Question

Passes through the point (0,6) and has a slope of -2/3

Answer 1

Answer:

$y=-\frac{2}{3}x + 6$

Step-by-step explanation:

We are given that a line has a slope of -2/3 and passes through the point (0,6)

We want to write the equation of this line; there are 3 forms of the line that we can use:

• Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
• Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negative
• Slope-point form, which is $y-y_1=m(x-x_1)$, where m is the slope and $(x_1, y_1)$ is a point

All though while writing the equation of the line in any of these ways is acceptable, the most common way is to write it in slope-intercept form, so let's do it that way.

As we are already given the slope, we can immediately substitute m with that value.

Replace m with -2/3:

y = -2/3x + b

Now we need to find b.

As the equation passes through the point (0, 6), we can use it to help solve for b.

Substitute 0 as x and 6 as y.

6 = -2/3(0) + b

Multiply

6 = 0 + b

Add

6 = b

Substitute 6 as b.

y = -2/3x + 6

Topic: finding the equation of the line

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