Question

Which is an equation of the line that passes through the point (1,4) and has a slope of 3? A. y = 3x + 4 B. I = 1 + 4 y $ C. y = 3x - 1 D.y = 3x + 1

Answer 1

Problem: Which is an equation of the line that passes through the point (1,4) and has a slope of 3?

Solution

Remember that the canonical form of the line is given by the

following equation:

y = mx + b

where m is the slope of the line and b is the y-coordinate of the y-intercept. Now, in this case, we have that m = 3. Then our canonical form of the line would be:

y = 3x +b

Now, take the point (1,4) = (x,y) and replace it on the above equation, that is:

4 = 3(1) + b

this is equivalent to

4 = 3 + b

solve for b:

b = 4-3 = 1

then, we can conclude that b = 1 and our canonical form of the line would be:

y = 3x+1

that is, an equation of the line that passes through the point (1,4) and has a slope of 3 is:

y = 3x+1