Find, in the form y=mx +c, the equation of the straight line with the given gradient which passes through the given point. gradient 3, point (1,2)

gradient -1, point (5,3)

gradient 4, point (-2,-3)

for first

Step-by-step explanation:

here

slope (m)=3

point=(1,2)=(x1,x2)

equation of straight line

(y-y1)=m(x-x1)

or 3x-y+1=0

so y= 3x+1

now do all of the question like this

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions