Find the y-intercept of the line: 6x – 3y +6=0

Mathematics

1 answer:

monitta3 years ago

6 0

Answer:

Step-by-step explanation:

The y-intercept exists where the x coordinate is 0. Therefore, we can find it by plugging in a 0 for x and solving for y:

6(0) - 3y + 6 = 0 and

-3y + 6 = 0 and

-3y = -6 so

y = 2

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Write an equation of the line below.

Lubov Fominskaja [6]

Answer (<u>assuming it can be in slope-intercept form)</u>:

$y = \frac{4}{5} x$

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula $m = \frac{y_2-y_1 }{x_2-x_1}$ and substitute the x and y values of two points on the line into it. We can see that the line passes through (0,0) and (5,4), so let's use those points for the formula and solve:

$m = \frac{4-0}{5-0} \\m = \frac{4}{5}$

So, the slope is $\frac{4}{5}$ .

2) Next, identify the y-intercept of the line. The y-intercept is the point at which the line intersects the y-axis. We can see that the line intersects the y-axis at (0,0), so that must be the y-intercept.

3) Now, write the equation of the line in slope-intercept form using the $y = mx + b$ format. The number in place of $m$ represents the slope, so substitute $\frac{4}{5}$ in its place. The number in place of $b$ represents the y-intercept, so substitute 0 in its place. This gives the following answer and equation: