Write the equation of the line that fits the given conditions. 14. Parallel to 3x-2y=10 and passes through the point (2,2), Write in standard form and slope-intercept form.

Answer:

Step-by-step explanation:

Since the lines are parallel to each other that means they have the same gradient. So use the gradient formula y=mx+c where m is the gradient rearrange 3x-2y=10 using the formula to become -2y=-3x +10

divide both sides by -2 so that m=1.5. It passed through the point (2,2) use the equation of a line formula to find the the answer.

[{y - 2}/{x -2}=1.5

cross multiply to get 1.5x-y=1

hope that helps

Final answer:

The equation of the line parallel to 3x - 2y = 10 and passes through the point (2,2) is y = 1.5x -1 in slope-intercept form, and 3x - 2y = -2 in standard form.

Explanation:

First, we must find the slope of the line parallel to the given line 3x - 2y = 10. The slope of this line, written in the form ax + by = c, is -a/b, so the slope is -3/(-2) = 1.5. The equation of the line we want to find has this same slope. This is because parallel lines have the same slope.

To find our line, we use the point-slope form of an equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging in given point (2,2) and the slope 1.5, the equation becomes y - 2 = 1.5(x - 2). Simplifying it, we get y - 2 = 1.5x - 3. Adding 2 to both sides gives our line in slope-intercept form: y = 1.5x -1.

To express the equation in standard form, we manipulate the equation to be in the form Ax + By = C. Multiplying the equation by 2 to remove fractions gives us y * 2 = x * 3 - 2, so the line in standard form is 3x - 2y = -2.

Learn more about Line Equations here:

brainly.com/question/35492661

#SPJ3