What is an equation of the line, in slope intercept form, that passes through the given point and has the given slope? point: (11,3); slope: 4/11

answer: y - 3 = 4/11(x - 11)

step-by-step explanation:

the equation of a straight line can be represented in the point slope form as

y - y1 = m( x - x1)

where

m = slope = (change in the value of y in the vertical axis) / (change in the value of x in the horizontal axis)

the given slope of the line is 4/11 and the point through which the line passes is (11,3)

we would substitute m = 4/11, x1 = 11 and y1 = 3 into y - y1 = m( x - x1) to get the equation in the point slope form. it becomes

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

for the slope intercept form, the equation is y = mx + c

where c is the intercept. to find c, we will substitute

m = 4/11, x = 11 and y = 3 into y = mx + c. it becomes

3 = 4/11 × 11 + c

3 = 4 + c

c = 3 - 4 = -1

the equation becomes

y = 4x/11 - 1

is there answer choices?

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.