Question

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-1,6) and parallel to x + 3y = 7.a) The equation of the line in slope-intercept form is.(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

Answer 1

To write the equation of a line passing through a given point and parallel to another line, we need to find the slope and the y-intercept. For this problem, the equation of the line passing through (-1,6) and parallel to x + 3y = 7 is y = (-1/3)x + 7/3 in slope-intercept form and 2x - 3y = 21 in standard form.

Step-by-step explanation:

To write the equation of a line in slope-intercept form, we need to find the slope and the y-intercept. Since the line is parallel to the given line, it will have the same slope. The given equation is x + 3y = 7. To find the slope, we can rearrange the equation in the form y = mx + b, where m is the slope and b is the y-intercept.

From the given equation, rearranging to slope-intercept form, we have:

3y = -x + 7

y = (-1/3)x + 7/3

So, the equation of the line in slope-intercept form is y = (-1/3)x + 7/3.

To write the equation in standard form, ax + by = c, we can multiply the equation by 3 to get rid of the fractions:

3y = -x + 7

-x - 3y = -x(3) + 7(3)

-x - 3y = -3x + 21

3x - x - 3y = 21

2x - 3y = 21

So, the equation of the line in standard form is 2x - 3y = 21.

Answer 2

`y=(1)/(3)x+(19)/(3)`

Step-by-step explanation:

Linear equations are represented in slope-intercept form by the following equation:

`\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=\text{ y-intercept} \end{gathered}`

If the line is parallel to x+3y=7, it means they have the same slope. Then, the slope would be;

`\begin{gathered} x+3y=7 \\ y=(x)/(3)-(7)/(3) \\ \text{ Slope is the coefficient that goes with the ''x''} \\ \text{Slope}=\text{ }(1)/(3) \end{gathered}`

Then, to find the y-intercept of the equation, substitute the slope and the given point, solve for b:

`\begin{gathered} 6=(1)/(3)(-1)+b \\ b=6+(1)/(3) \\ b=(19)/(3) \end{gathered}`

Hence, the equation would be:

`y=(1)/(3)x+(19)/(3)`