What is the difference between slope-intercept form of a line, y = mx + b and point-slope form of a line $$? Discuss the information

''Point slope form and slope intercept form are both ways of expressing the equation of a straight line. Point slope form emphasizes the slope and ANY point on the line. Slope intercept form just shows the slope and the y-intercept of a line.''    -Kahn Academy

Step-by-step explanation:

[tex]y=\frac{2}{5}x-8[/tex]

Step-by-step explanation:

By definition, the equation of the line in  slope-intercept form of is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

Then, given the slope 2/5 and the point, (-10, -5), you can calculate the value of b by susbtituting and solve for it:

[tex]-10=\frac{2}{5}(-5)+b\\ -10=-2+b\\b=-8[/tex]

Substitute this value and the slope into the equation. THerefore, you obtain:

[tex]y=\frac{2}{5}x-8[/tex]

y = -4x+9

Step-by-step explanation:

Slope-intercept form:

The equation of line is given by:

[tex]y=mx+b[/tex]           .....[1]

where,

m is the slope of line

b is the y-intercept.

As per the statement:

Given: The rate of change = -4

Substitute in [1] we have;

[tex]y = -4x+b[/tex]

Substitute the values of  any (x, y) from the given table.

Let x = -1 and y = 13

then;

13 = -4(1-)+b

⇒13 = 4+b

Subtract 4 from both sides we have;

[tex]9= b[/tex]

or

b = 9

⇒the equation become, y = -4x+9

Therefore, the slope-intercept form of this line is,  y = -4x+9

#1 . Point slope form and slope intercept form are both ways of expressing the equation of a straight line.

#2. Point slope form emphasizes the slope and ANY point on the line.

#3 . Slope intercept form just shows the slope and the y-intercept of a line.

Step-by-step explanation:

y=negative 2x+1

Step-by-step explanation:

rise over run negative 14 over 7 equals negative 2 and the y intercept is 1

The slope intercept form of this line is y = -4x + 9.