Write the standard form of the line that is parallel to 2 x + 3 y = 4 and passes through the point (1, -4). include your work in your final answer. type your answer in the box provided or use the upload option to submit your solution.

Step-by-step explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope we can find from the standard equation. We will chose point-slope since we have a point and can find the slope.  We can then convert into standard.

Point slope:

We must find the slope by converting the standard form into slop-intercept.

We rearrange in y=mx+b form to .

Since parallel lines have the same slope is the slope for our line. We will now use point slope form.

We will substitute and .

" alt="y+4=-\frac{2}{3}x+\frac{2}{3} \\y+4-4=-\frac{2}{3}x+\frac{2}{3}-4\\y=-\frac{2}{3}x+\frac{2}{3}-4\\y=-\frac{2}{3}x+\frac{2}{3}-\frac{12}{3} \\\frac{2}{3}x+y=-\frac{2}{3}x+-\frac{2}{3}x-\frac{10}{3}" />" />

This simplifies to .

To be in standard form, the coefficients of x and y must not be 0 or any fractions. The coefficient of x muxt be positive. To meet these requirements, we multiply the entire equation by 3.

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