Write an equation in slope intercept form for the line described

Through (-1,4) parallel to x+3y=5

I got y=1/3x + 13/3

To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope.

First, let's rearrange the given equation, x + 3y = 5, into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

x + 3y = 5

3y = -x + 5

y = (-1/3)x + 5/3

The slope of the given line is -1/3.

Since the line we want to find is parallel to this line, it will also have a slope of -1/3.

Now, we can use the point-slope form of a linear equation to find the equation of the line passing through the point (-1, 4):

y - y1 = m(x - x1)

Plugging in the values, we have:

y - 4 = (-1/3)(x - (-1))

y - 4 = (-1/3)(x + 1)

y - 4 = (-1/3)x - 1/3

To convert this equation to slope-intercept form, isolate y:

y = (-1/3)x - 1/3 + 4

y = (-1/3)x - 1/3 + 12/3

y = (-1/3)x + 11/3

Therefore, the equation of the line passing through (-1, 4) and parallel to x + 3y = 5 is y = (-1/3)x + 11/3 in slope-intercept form.

To find the equation in slope intercept form for a line parallel to a given line, we need to determine two things: the slope of the line we want and the y-intercept.

First, we need to find the slope of the line x + 3y = 5. We can rearrange the equation into slope-intercept form (y = mx + b) to find the slope. To do this, subtract x from both sides to isolate 3y, and then divide by 3:

x + 3y = 5
3y = -x + 5
y = (-1/3)x + 5/3

The slope of the given line is -1/3.

Since we want to find a line parallel to this one, the parallel line will also have a slope of -1/3.

Now, we have the slope (-1/3) and a point on the line (-1, 4). We can use the point-slope form of a line to determine the equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Using the values: x1 = -1, y1 = 4, and m = -1/3, we can substitute them into the point-slope form:

y - 4 = (-1/3)(x - (-1))

Simplifying further:

y - 4 = (-1/3)(x + 1)

Distributing the -1/3:

y - 4 = (-1/3)x - 1/3

Finally, we can rearrange the equation into slope-intercept form by isolating y:

y = (-1/3)x - 1/3 + 4
y = (-1/3)x + 11/3

Therefore, the equation in slope-intercept form for the line parallel to x + 3y = 5 and passing through the point (-1, 4) is y = (-1/3)x + 11/3.

Since the new line is parallel to x+3y=5

it differs only in the constant:
x+3y=c
plug in (-1,4) to find c and you are done